Matrix/C/Special unitary group/Definition

Special unitary group

A unitary ${}n\times n$-matrix ${}M\in \operatorname {GL} _{n}\!{\left(\mathbb {C} \right)}$ fulfilling

${}\det M=1\,$

is called a special unitary matrix. The set of all special unitary matrices is called Special unitary group; it is denoted by ${}\operatorname {SU} _{n}$.